Abstract

An analog of an optically bistable device made constructed from both optical and electronic components is used to study chaos. This hybrid optically bistable system has a delay in the feedback so that the response time of the electronics is much faster than the feedback time. Such a system is unstable and shows pulsations and chaos. The character of the pulsations change as the gain of the amplifier or the input laser power is increased. These changes make up the period doubling route to chaos. Not all of the waveforms of an ideal period doubling sequence are observed. This truncation of the period-doubling sequence in the device is investigated as a function of the noise present in the system. Increasing the noise level decreases the number of period doublings observed. In the chaotic regime waveforms other than those predicted are observed. These waveforms are the frequency-locked waveforms seen in an earlier experiment which we find to be modified versions of the typical period-doubled waveforms. The transitions between these waveforms are discontinuous, and show hysteresis loops. By the introduction of an external locking signal, we are able to stabilize waveforms in the neighborhood of the discontinuous transitions. By so doing we show that the transitions among the branches are due to their lack of stability. The transitions are thus not strictly first-order nonequilibrium phase transitions, since in that case the branches cease to exist at the transition point. Since the path to chaos is nonunique, the types of chaos that are observable are also nonunique. To suggest a way to distinguish between different types of chaos and also to provide a tool for the study of chaos in other systems, we propose an operational test for chaos which leads to a straightforward experimental distinction between chaos and noise. We examine this test using the hybrid device to show that the method works. The test involves repeated measurement of the initial transient of a system whose initial condition is fixed. This method could be used to determine the existence of chaos in faster optical systems.

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